Rewrite as a simplified fraction. ${0.2\overline{4} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 24.4444...\\ 10x &= 2.4444...\end{align*}}$ Subtracting the two equations, we have: ${90x = 22}$ ${x = \dfrac{22}{90}} $ ${x = \dfrac{11}{45}} $